Chapter 7. Newton’s Third Law

1. Chapter 7. Newton’s Third Law Chapter Goal: To use Newton’s third law to understand interacting objects.

2. Ch. 7 – Student Learning Objectives • To learn how two objects interact. • To identify action/reaction pairs of forces. • To understand and use Newton’s third law. • To understand how to use propulsion forces and tension forces.

3. OMIT section 7.2 (#1-7) in workbook, but don’t xxxxx it out • We’ll do a modification during class.

4. Newton’s Third Law

5. Action-reaction Pair If object A exerts a force on object B, then object B exerts a force on object A. The pair of forces (due to one interaction), is called an action/reaction pair. The action/reaction pair will never appear in the same free body diagram.

6. Tactics: Analyzing interacting objects

7. Example - analyzing interacting objects A person pushes a large crate across a rough surface. • Identify the objects that are systems of interest • Draw free-body diagrams for each system of interest. • Identify all action/reaction pairs with a dashed line.

8. Forces involved in pushing a crate – FBD of person and crate

9. Propulsion Force • The force label fp shows that the static friction force on the person is acting as a propulsion force. • This is a force that a system with an internal source of energy uses to drive itself forward.

10. Propulsion forces

11. Freebody Diagrams – Workbook exercises 1-7 Draw a freebody diagram of each object in the interacting system. Show action/reaction pair with red/orange dotted lines. Draw force vectors in another color. Label vectors with standard symbols. Label action/reaction pairs FAonB , FBonA for example.

12. A fishing line of negligible mass lifts a fish upward at constant speed. The line and the fish are the system, the fishing pole is part of the environment. What, if anything, is wrong with the free-body diagrams?

13. A fishing line of negligible mass lifts a fish upward at constant speed. The line and the fish are the system, the fishing pole is part of the environment. What, if anything, is wrong with the free-body diagrams? The gravitational force and the tension force are incorrectly identified as an action/reaction pair. The correct action reaction pair is…? Action/reaction pairs are never on the same free body diagram. Mass of line considered negligible so no weight force necessary.

14. Acceleration constraint • An acceleration constraint is a well-defined relationship between the acceleration of 2 (or more) objects. • In the case shown, we can assume ac =aT = ax

15. Is there an acceleration constraint in this situation? If so, what is it? The pulley is considered to be massless and frictionless.

16. Answer: Acceleration constraint is: aA = -aBThe actual signs may not be known until the problem is solved, but the relationship is known from the start.

17. Workbook exercises 12-16 + “17” 17

18. answers a2kg = -.5a1kg

19. Boxes A and B are sliding to the right across a frictionless table. The hand H is slowing them down. The mass of A is larger than the mass of B. Rank in order, from largest to smallest, the horizontal forces on A, B, and H. Ignore forces on H from objects not shown in the picture.

20. Boxes A and B are sliding to the right across a frictionless table. The hand H is slowing them down. The mass of A is larger than the mass of B. Rank in order, from largest to smallest, the horizontal forces on A, B, and H. FB on H = FH on B > FA on B = FB on A from Newton’s 2nd and 3rd Laws

21. Problem-Solving Strategy: Interacting-Objects Problems

22. EOC #8 Two strong magnets each weigh 2 N and are on opposite sides of the table. The table, by itself, has a weight of 20 N. The long range-range attractive force between the magnets keeps the lower magnet in place. The magnetic force on the lower magnet is 3 times its weight. a. Draw a fbd for each magnet and table. Use dashed lines to connect all action/reaction pairs. b. Find the magnitude of all forces in your fbd and list them in a table.

23. EOC #8 Upper Table Lower

24. FBDs for EOC 8

25. EOC #8 - Answer

26. Ranking Task – Pushing blocks Block 1 has a mass of m, block 2 has a mass of 2m, block 3 has a mass of 3m. The surface is frictionless. Rank these blocks on the basis of the net force on each of them, from greatest to least. If the net force on each block is the same, state that explicitly

27. Ranking Task – Pushing blocks Answer: 3 2 1 Reason: ΣF = ma. Acceleration is equal for all blocks.

28. EOC #10 Block 1 has a mass of 1 kg, block 2 has a mass of 2 kg, block 3 has a mass of 3 kg. The surface is frictionless. a. Draw a fbd for each block. Use dashed lines to connect all action/ reaction pairs. b. How much force does the 2-kg block exert on the 3-kg block? c. How much force does the 2-kg block exert on the 1-kg block?

29. EOC #10- Answer b. How much force does the 2-kg block exert on the 3-kg block? – 6N c. How much force does the 2-kg block exert on the 1-kg block? – 10N

30. Page 163, 2nd Ed (Found in Chapter 5, 1st ed)

31. Interacting systems problem (EOC #35) A rope attached to a 20 kg wooden sled pulls the sled up a 200 snow-covered hill. A 10 kg wooden box rides on top of the sled. If the tension in the rope steadily increases, at what value of tension will the box slip?

32. Interacting systems problem (EOC #35) Find the max tension in the rope, so the box does not slip. What are the objects of interest?What kind of axes for the FBD for each?Acceleration constraints?Draw FBDs, with 3rd law pairs connected with dashed lines.

33. Box: 3 forces Sled: 6 forces 0.06

34. I suggest starting with the equations for the sled, since the unknown of interest is found there. • Identify quantities in sled equations that you can find by solving box equations. • Solve box equations. • Return to sled equations with newfound booty. • Plug and chug. 0.06

35. Interacting systems problem (EOC #35) A rope attached to a 20 kg wooden sled pulls the sled up a 200 snow-covered hill. A 10 kg wooden box rides on top of the sled. If the tension in the rope steadily increases, at what value of tension will the box slip? Answer: 155 N.

36. The Massless String Approximation A horizontal forces only fbd for the string: TAonS TBonS ● ΣF = TBonS – TAonS = ma. If string is accelerating to the right TBonS = TAonS + ma

37. The Massless String Approximation Often in physics and engineering problems the mass of the string or rope is much less than the masses of the objects that it connects. In such cases, we can adopt the following massless string approximation: This allows the objects A and B to be analyzed as if they exert forces directly on each other.

38. Pulleys If we assume that the string is massless and the pulley is both massless and frictionless, no net force is needed to turn the pulley. TAonB and TBonA act “as if” they are an action/reaction pair, even though they are not acting in opposite directions.

39. Pulleys • In this case the Newton’s 3rd law action/reaction pair point in the same direction! T 100kg on m Tm on 100kg

40. All three 50 kg blocks are at rest. Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1? • Equal to • Greater than • Less than

41. All three 50 kg blocks are at rest. Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1? • Equal to • Greater than • Less than

42. In the (moving) figure to the right, is the tension in the string greater than, less than, or equal to the weight ofblock B? • Equal to • Greater than • Less than

43. In the figure to the right, is the tension in the string greater than, less than, or equal to the weight ofblock B? • Equal to • Greater than • Less than

44. Interacting systems problem (EOC #40) A 4.0 kg box (m) is on a frictionless 350 incline. It is connected via a massless string over a massless, frictionless pulley to a hanging 2.0 kg mass (M). When the box is released: • Which way will it go George? • What is the tension in the string? 4.0 kg 350

45. Interacting systems problem (EOC #40) a. Which way will it go? Even if you have no clue, follow the plan! What are the objects of interest?What kind of axes for the FBD for each?Acceleration constraints??Draw FBDs, with 3rd law pairs connected with dashed lines. 4.0 kg 350

46. Interacting systems problem (EOC #40) How do you figure out which way the system will move, once m is released from rest? massless string approx. allows us to join the tensions as an “as if” interaction pair

47. Interacting systems problem (EOC #40)

48. Interacting systems problem (EOC #40) a = - 0.48 m/s2, T = 21 N. Which way is the system moving? How does the tension compare to the tension in the string while the box was being held? Greater than, less than, equal to?

49. EOC # 33 The coefficient of static friction is 0.60 between the two blocks in the figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force Fcauses both blocks to slide 5 meters, starting from rest. Determine the minimum amount of time in which the motion can be completed without the upper block slipping.

50. EOC # 33 The coefficient of static friction is 0.60 between the two blocks in the figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force Fcauses both blocks to slide 5 meters, starting from rest. Determine the minimum amount of time in which the motion can be completed without the upper block slipping.